Functional dependency in DBMS is a constraint between two set of attributes. In a relational database schema having n attributes, there exists a universal relation R = {A1, A2, A3, ..., An}. A functional dependency is denoted by X→Y, where X and Y are subset of R. In relation R, attribute (or set of attributes) Y is functionally dependent to attribute X, means value of X can uniquely determine the value of Y.
The abbreviation of functional dependency is FD or f.d.
The left hand side is called determinant and right hand side is dependent.
Consider the below relation, in this each value of X uniquely determines value of Y
Now consider the below table, here there are two 1s in X attribute but both determines two different value of Y, this violates functional dependency X->Y.
Inference Rules for Functional Dependencies
In a database schema, F is a set of functional dependency. But are some other dependency that can be inferred or deduced from functional dependencies FD in F.
The set of all dependencies including F as well as other dependencies inferred from F are known as closure of F and it is denoted by F*
For example: {Emp_id → {Emp_name, Emp_salary, Emp_mobile}}
Emp_mobile → {Emp_name, Emp_salary}
Following dependencies can be inferred from above two FD
Emp_mobile → Emp_name
Emp_id → Emp_id
The following rules are inference rules for functional dependency.
- Reflexive rule
If Y ⊆ X, then X →Y
- Augmentation rule
If {X →Y}, then XZ →YZ
- Transitive rule
If {X →Y, Y →Z}, then X →Z
- Decomposition, or projective, rule
If {X →YZ}, then X →Y
- Union, or additive, rule
If {X →Y, X →Z}, then X →YZ
- Pseudotransitive rule
If {X →Y, WY →Z}, then WX →Z
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